SOLVABILITY OF COMMUTATIVE RIGHT-NILALGEBRAS SATISFYING (b(aa))a = b((aa)a)

Abstract

We study commutative right-nilalgebras of right-nilindex four satisfying the identity (b(aa))a = b((aa)a). Our main result is that these algebras are solvable and not necessarily nilpotent. Our results require characteristic 6 = 2, 3, 5.2000 Mathematics Subject Classification : 17 A30.